Given the voxelized point cloud, we calculate the center location \(P_{c}\)  of every voxel. To accelerate processing speed, we locate non-empty voxels and aggregates local features only on these voxels. For a non-empty voxel \((u,v,w)\) , we use the cell center as query position and gather K neighbors through K-nearest-neighbor(KNN).
We adopt the dilated point convolution strategy as proposed in [1]}, in which \(K\cdot n\)  nearest neighbors and every \(n-th\)  neighbor is selected. The feature \(f\)  for voxel \((u,v,w)\)  is the weighted summation of all K neighbors.
\(f_{u,v,w} = \sum _k^K l_k * f_k\) 
